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What is known about primorial and factorial minus one prime?

Mathematics Asked by Enzo Creti on December 25, 2021

$324$ is an example of an integer such that both $324!-1$ and $primorial(324)-1$ are primes.
Are there other examples?
Is there some condition to be $n! – 1$ and $primorial(n) -1$ both primes?

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